MATH1850 Midterm 2
Nov, 2015
v1 (1, 1, 2, 4) ,
v 3 ( 1, 1, 11, 4) are linearly independent or
1. (8 marks) Determine whether the vectors
v 2 ( 2, 3, 1, 8) , and
dependent. NOTE: You must show all your calculations involving matrices, and you
MUST show eac
1 2 1 k1
1. (9 marks) Consider the system 1 1 1 k 2 . Find conditions, if they exist,
0
1
2 k 3
on the numbers k1 , k 2 , and k 3 such that the given system has
a) No solution
b) A unique solution
c) Infinitely many solutions
NOTE: Clearly label all y
Chapter 3.1
(a) Two equivalent vectors must have the same initial point. = False
(b) The vectors (a, b) and (a, b, 0) are equivalent. = False
(c) If k is a scalar and v is a vector, then v and kv are parallel if
and only if k 0. = False
(d) The vectors v
OBJECTIVES:
Section 4.3: By the end of this section, you will be able:
to determine whether a set of vectors is linearly dependent or linearly independent
to state that a set of vectors S is linearly dependent if and only if at least one of the
vectors in
OBJECTIVES:
Section 4.2: By the end of this section, you will be able:
to give the definition of a `subspace of a vector space" , and determine whether or not a
given subset of a vector space is a subspace
to determine whether or not a vector, w is a line
Linear Algebra Midterm 1- V1
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Linear Algebra Midterm 1- V1
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Linear Algebra Midterm 1- V1
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Linear Algebra Midterm
Linear Algebra Midterm 1- v6-Solutions
MATH1850 Midterm 1
October, 2010
1. (3 marks each; total 6 marks) Solve the linear systems associated with the
following augmented matrices. Hint: They are already either in reduced row-echelon or
row-echelon form fo
MATH1850U: Chapter 1 cont
1
LINEAR SYSTEMS cont
Introduction to Systems of Linear Equations (1.1; pg.2) cont
Recall: Last day, we talked about systems of 2 equations in 2 unknowns, and 3 equations
in 3 unknowns.
Ok, finally, lets extend this even furthern
MATH1850U: Chapter 1
1
LINEAR SYSTEMS
Application Balancing Chemical Equations: Write a balanced equation for the given
chemical reaction: CO2 + H2O C6H12O6 + O2 (photosynthesis)
Application Population Migration: A country is divided into 3 demographic re
MATH1850U: Chapter 1 cont.
1
LINEAR SYSTEMS cont
Gaussian Elimination (1.2; pg. 11) cont.
Recall: Last day, we introduced Gaussian and Gauss-Jordan Elimination for rowreducing a matrix. Lets get some more practice at this.
More Examples: Lets do some more
Linear Algebra Midterm 1- v2-Solutions
MATH1850 Midterm 1
October, 2010
1. (3 marks each; total 6 marks) Solve the linear systems associated with the
following augmented matrices. Hint: They are already either in reduced row-echelon or
row-echelon form fo